Did they back either side? Did they receive refugees? Did they have substantial numbers of citizens go to fight?
The Prime Minister of Portugal at the time, António de Oliveira Salazar, was very supportive of Franco's Nationalists pretty much from the get go. His government was authoritarian in nature and had poor relations with the Spanish Republic's left-wing government. In fact many left-wing Portuguese activists had fled to Spain due to Salazar's heavy-handed approach to quelling opposition (mainly communist but also socialist, anarchist, liberal etc).
In terms of aid they provided ammunition and logistical support to Franco's forces from the beginning of the war onward. There was also direct involvement by Portuguese volunteers (referred to as Viriatos, named after the Lusitanian leader Viriatus), the number of which is debated but usually given as 8,000 to 12,000. Some joined the Spanish Foreign Legion directly but others also joined various militias. There was also a Portuguese Military Observation Mission which although mainly serving a non-combat advisory role had some involvement through its airforce which took part in combat missions alongside the Nationalist forces.
In 1938 Salazar's government officially recognised Franco's government and after the war was important in supporting Franco's new regime to other European powers, chiefly France and the UK.
Source: Mostly "Franco's International Brigades: Adventurers, Fascists, and Christian Crusaders in the Spanish Civil War" By Christopher Othen which I found extremely interesting and would recommend to anyone interested in this subject.